As suggested in [1]}, our implementation of the two-level ADMM uses \(\omega = 0.75\) , \(\gamma = 1.5\) , \([\underline{\lambda }, \bar{\lambda }] = [-10^6, 10^6]\) , \(\beta ^1 = 1000\) , \(\rho ^k = c_1 \beta ^k\) , and the \(k^\mathrm {th}\)  level inner-level loop is terminated based on [1]} with \(\epsilon _3^k = \sqrt{2n_g(T-1)}/(c_2 k \rho ^k)\) , where \(n_g\)  is the number of generators and all other symbols refer to the notation in [1]}.
After trying \((c_1, c_2) \in \lbrace 2 \times 10^f : f = -6, -4, -2, 0, 2\rbrace  \times \lbrace 1, 1000\rbrace \) , we set
\(c_1 = 2\times 10^{-4}\)  and \(c_2 = 1000\) , since it produced the smallest infinity norm of the combined primal and dual residual vector [1]} after 50 cumulative iterations.
We set the tolerance \(\epsilon = 10^{-8}\)  in Algorithm REF .
